Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Of a fourvector in representing a point in spacetime, having a positive fourvector norm.
 adj. (of the interval between two events in spacetime) Having overlapping light cones, so that information can pass from one to the other, and one can be envisaged as a cause of the other.
Etymologies
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Examples

The far future of our universe is therefore representable by de Sitter spacetime, and in this type of spacetime the future timelike boundary is a spacelike hypersurface.

Now, in an open or flat FriedmannRobertsonWalker cosmological model with no cosmological constant, whilst the past 'BigBang' singularity corresponds to a spacelike hypersurface in the boundary of the conformal compactification, the future timelike infinity corresponds to a single point.

The boundary of the conformal compactification contains components which correspond to singularities, and components which correspond to spacelike infinity, timelike infinity, (and null infinity).

The math is almost identical to my example, except that you get a timelike interval instead of a spacelike one.

The interval is zero between two points within a single lap, but it is nonzero (and timelike) when you take points on two different laps.

The result is a nonzero interval, spacelike for two photons emitted simultaneously from a source and timelike between different points on the worldline of a photon bouncing between mirrors.

And Frank Tipler, in his youth, did some pioneering research on closed timelike curves in general relativity, so he has credentials as an honest physicist.
Accusations and Assumptions: Another MythicistCreationist Parallel

But there are soulutions that allow 'closed timelike curves'  travel backwards in time, at least back to a defined origin.

At least, there would only be flashing lights if you brought along some strobes, and decided to start them flashing as you traveled along your closed timelike curve.

So: if there were a closed timelike curve, we would age along it, and feel older when we finished our journey than when we started it, just as for any other journey.
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